Electrochimica Acta 56 (2011) 4735–4743

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Electrochimica Acta

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Neutron depth profiling technique for studying aging in Li-ion batteries

Shrikant C. Nagpurea, R. Gregory Downingb, Bharat Bhushana,!, S.S. Babuc, Lei Caod

a Nanoprobe Laboratory for Bio & Nanotechnology and Biomimetics (NLBB), Ohio State University, 201 West 19th Avenue, Columbus, OH 43210, USAb National Institute of Standards and Technology (NIST), Gaithersburg, MD 20899, USAc Department of Material Science and Engineering, Ohio State University, Columbus, OH 43210, USAd Department of Mechanical and Aerospace Engineering, Ohio State University, Columbus, OH 43210, USA

a r t i c l e i n f o

Article history:Received 2 December 2010Received in revised form 28 January 2011Accepted 8 February 2011Available online 15 February 2011

Keywords:Li-ion batteriesAgingLithium concentrationNeutron depth profiling

a b s t r a c t

During operation of a Li-ion cell, lithium diffuses in and out of the solid phase anode and cathode. Mea-suring the lithium concentration within the electrodes of the cell over its operational life could providekey information for understanding the loss of active lithium and the associated aging mechanisms. Con-centration profiles of lithium in a cell are difficult to measure with traditional spectroscopic techniques.Here, neutron depth profiling was used to measure lithium near-surface concentration profiles along theanode and cathode strips in off-the-shelf cylindrical Li-ion batteries as a function of the aging process. Abuildup of the surface concentration of lithium was found in graphite anode as well as a general decreasein the intercalation efficiency in lithium iron phosphate cathode material with aging.

© 2011 Elsevier Ltd. All rights reserved.

1. Introduction

Demand continues to grow world-wide for environmentallyfriendly vehicles such as hybrid electric vehicles (HEV), plug-inhybrid electric vehicle (PHEV), and electric vehicles (EV). In partor in whole, each of these vehicles rely on advanced battery tech-nology for clean and transportable energy. Though various batterychemistries such as lead-acid and nickel metal hydride have beencommercially used for a period of time, lithium ion battery tech-nology is emerging as the front runner for energy storage systems.Lithium ion batteries deliver high energy and power capacity withminimal maintenance; however, battery performance issues arethe focus of much research.

The first lithium ion battery was commercially introduced bySony in 1990 which had LiCoO2 as the cathode. Since then therehave been several different types of lithium ion batteries basedon different cathode materials. These include layered structuressuch as LiMn0.5Ni0.5O2, LiMn0.5"ıNi0.5"ıCo2ıO2, Li1"xNi1"yCoyO2or spinel structured cathodes such as Li[Mn2]O4 [1]. However, themore recent olivine structured LiFePO4 cathode material has showngreat potential for applications in EV and PHEV. Apart from beingnon-toxic and relatively inexpensive, LiFePO4 has become populardue to its operating potential of 3.4 V and high specific capacity of160 mAh g"1 [2].

! Corresponding author. Tel.: +1 614 292 0651.E-mail address: bhushan.2@osu.edu (B. Bhushan).

In automotive applications, the charging and discharging ofthe battery is controlled and managed by a battery managementsystem (BMS). The BMS is composed of hardware and softwarecomponents and is responsible for safe operation of the battery.According to United States Advanced Battery Consortium (USABC),a 42 V battery in a hybrid electric vehicle (HEV) should have a calen-dar life of 15 years [3]. Electric vehicles (EV) should have a batterysystem that can last for 10 years [4]. In terms of cycles, 1000 cycles at80% depth-of-discharge are expected in EV [4], and 300,000 cyclesat 50 Wh are expected in a plug-in HEV [5]. Thus, much of theresearch efforts have been in the area of understanding the agingmechanisms in these batteries.

The capacity (range) and power (performance) capabilities ofthese batteries decrease when subjected to the charging and dis-charging cycles in automobiles. This degradation of capacity/poweror “aging” is a result of several simultaneous physiochemicalprocesses that occur within the electrode, electrode–electrolyteinterface, and within the electrolyte. The aging of these batteries isa very complex phenomenon. Various electrochemical processes,including intercalation of lithium ions into layered graphite anodeand cathode materials, as well as mass transport of lithium ionthrough the electrolyte, occur simultaneously within the cell. Theseprocesses lead to different extent of degradation in materials prop-erties and the subsequent drop in overall performance of batteries.Therefore, it has been scientifically important to track the lithiumconcentration in the cathode and anode during aging process. Thecurrent work pertains to this critical need.

Aging of the LiFePO4 cathode has been studied by various tech-niques. Spectroscopy techniques such as energy dispersive X-ray

0013-4686/$ – see front matter © 2011 Elsevier Ltd. All rights reserved.doi:10.1016/j.electacta.2011.02.037

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spectroscopy (EDS) or electron energy loss spectroscopy (EELS)have been used to conduct the elemental analysis of the cath-ode material. Electron microscopic techniques have been usedto analyze phase change, structural changes, etc. Scanning probemicroscopy such as conductive atomic force microscopy (AFM)and surface resistance microscopy have been used for analysis ofsurface electrical properties [6,7]. These techniques deliver someuseful information about the changes in the cathode, but they failto address the issue of lithium transport or lithium concentrationwithin the cathode. The EDS technique is commonly used to iden-tify the atomic percent of the elements in the component. TheEDS detectors are very sensitive to impurities. To avoid repeatedexposure of the detectors to atmosphere, the detectors are main-tained under separate vacuum and separated from the columnvacuum in the electron microscope. The thin beryllium windowon the EDS detector absorbs low energy X-rays and thus preventsthe use of EDS in the detection of elements with an atomic num-ber less than five. Therefore, EDS also fails to detect Li in thecomponent.

Ziegler et al. [15] for first time used the nuclear reaction exper-iment to determine the concentration of boron impurity in siliconwafers. The sample was bombarded with a well-collimated beamof low energy neutrons in vacuum, and the emitted energizedparticles were analyzed using a charged-particle spectroscopy forthe concentration profile of the 10B in the sample. Later, Down-ing et al. [8] coined the term neutron depth profiling (NDP) forthis technique. Since then there have been several applicationsof this technique to other neutron sensitive light-weight iso-topes, some of which are listed by Downing et al. [9]. Biersackand Fink [30] were first to study the implantation of lithium insemiconductors using NDP. Later on Krings et al. [10] studiedlithium diffusion in electrochromic WO3 filmsusing NDP. Theycompared the secondary ion mass spectrometry (SIMS), elasticrecoil detection (ERD), and NDP techniques while profiling thelithium concentration along the depth of lithium intercalated thinelectrochromic WO3 films. They concluded that the NDP tech-nique has a very good depth resolution with high sensitivity andproves to be very useful over the other techniques because of itsnon-destructiveness. Lamaze et al. [11] have demonstrated theuse of NDP in two thin film battery materials. They profiled thelithium concentration in ion beam assisted deposition (IBAD) thinlithium phosphorus oxynitride films and thin lithium cobalt oxidefilms. The main advantage was again the non-destructive natureof the NDP technique. The study was limited to the depositedthin films rather than electrodes extracted from actual lithium ioncell.

Most recently, Whitney et al. [12] used NDP to profile the lithiumconcentration in a cathode of the Li-ion lab cells and an anode ofthe off-the-shelf Li-ion cells. The lithium transportation was stud-ied for storage of cells at different temperatures and cycling of thecells at different rates. They demonstrated a method to determinethe thickness of the solid electrolyte interface on a graphite anodein a LiFePO4 cell when stored for different lengths of time under dif-ferent temperatures. They also profiled the lithium concentrationin LiFePO4 and LiNi1/3Mn1/3Co1/3O2 cathodes after cycling for only100 cycles. This helped to understand the lithium distribution ininitial cycles but did not address the issue of lithium transportationduring the end of life of the cells.

In this paper, the NDP technique is applied to study the aging of acommercial off-the-shelf LiFePO4 based Li-ion cell during the agingprocess, including the end-of-life conditions, which has remainedas a challenge until now. A detailed analysis of the lithium con-centration in the anode and cathode is carried out. The lithiumconcentration profiles in the anode and cathode samples unagedand aged at different rates along the depth as well as concentrationgradients as a function of cycling current are determined. Further,

Table 1Different samples used to study the lithium concentration profile.

Sample Aging condition Residual capacity

C0 New – no aging 100%C1 1C, 0–10% SOC, 45 #C $80%C3 3C, 0–10% SOC, 45 #C $80%C4 4C, 0–10% SOC, 45 #C $80%C6 $6C, 60–70% SOC, 45 #C $80%C16 16C, 45–55% SOC, 45 #C $80%

SOC, state of charge.

it is investigated whether the lithium buildup on the surface of theanode or cathode occurred as the battery aged due to cycling.

2. Experimental details

2.1. Sample preparation

Commercial lithium ion cells used in these experiments have agraphite anode and a cathode comprising of LiFePO4 nanoparticles(40 nm–50 nm). Graphite is bonded onto a copper substrate, andlayers of LiFePO4 nanoparticles are bonded onto an aluminum sub-strate using a polyvinylidene difluoride (PVDF) binder. The anodeand cathode strips, with a separator in between, are rolled andthen packed into a can to form a cylindrical cell. The electrolyteused in this cell is a lithium hexafluorophosphate (LiPF6) salt in 1:1ethylene carbonate and dimethyl carbonate. The cell has an oper-ating voltage of 3.3 V and a nominal discharge capacity of 2.3 Ah.LiFePO4 has poor electronic conductivity (! = 2 % 10"9 S cm"1) [13].To improve the conductivity, the nanoparticles are coated with car-bon [14]. Table 1 describes the condition of the cells used in thisstudy. The effect of charging or discharging current rate (C-rate)on the lithium concentration was studied on cells #C1, C3, and C4cycled from 0% to 10% state of charge (SOC) with a C-rate of 1C, 3Cand 4C, respectively (1C-rate = 2.3 Ah). Two cells were cycled withhigher C-rates and at higher SOC to study the effect of the SOC onthe lithium concentration profiles. Cell C6 was cycled from 60% to70% SOC with 6C rate. Cell C16 was cycled with the highest C-rateof 16C from 45% to 55% SOC. All the cells were cycled at 45 #C. Acell that underwent only one complete charge–discharge cycle wasestablished as the baseline cell in our studies (C0). The cycling ofthe cells was terminated when the cells reached $80% of their ratedcapacity. This protocol was found to be consistent with the auto-motive industry standard, which considers a cell to be dead whenits capacity drops below 80% of the original rating [5].

The cells are completely discharged after they have reached the$80% of their rated capacity. The cylindrical cell was then openedin a glove box filled with argon atmosphere. The oxygen level wasmaintained at $88 ppm and the dew point was $"34 #C. The cellwas unrolled, and the long anode and cathode strips were sepa-rated. Each electrode strip was then divided into six sections asshown in Fig. 1. Section #1 is near the outer circumference andsection #6 is near the center of the cylindrical cell. The NDP mea-surements were performed on each section of all cells, but for claritythe results of only section #1, 3 and 5 are plotted in the figuresbelow in the paper.

2.2. NDP setup and technique

NDP is a non-destructive analytical technique based on theinteraction of an incident beam of neutrons with certain elements,such as lithium, throughout the sample. The cold neutrons aredelivered through a neutron guide to the NDP facility. In this work,the “cold” neutrons refer to neutrons with energy less than 5 meV.Since cold neutrons have extremely low energy and momentum,there is no center-of-mass motion in the neutron-lithium reac-

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Fig. 1. The electrode strip taken from each cell is physically divided into six sections.Section #1 originated farthest from the core and section #6 is nearest to the core ofthe cell.

tion. Furthermore, the neutron event rate is insufficient to causesignificant temperature rise in the sample nor is there significantradiation damage to the sample during the measurement period.All NDP experiments were conducted at the NIST Center for Neu-tron Research (NCNR). A schematic of the NDP facility is shown inFig. 2.

The sample is attached to an aluminum disk (Figs. 1 and 2)which is held vertically at the center of a vacuum chamber by thegrooves provided on the sample mount. The sample mount is ori-ented such that the sample faces the surface-barrier type chargedparticle detector. The detector has an active area of 150 mm2 andis placed slightly more than 10 cm from the neutron beam-spot onthe sample. A $0.8 cm2 area of the sample is illuminated by the coldneutron beam entering the vacuum chamber. Upon the absorptionof the neutron by the elemental atom in the sample, monoener-getically charged alpha and triton particles are emitted and traveldiametrically opposite from the site of the reaction. More specif-ically, when the neutron reacts with the 6Li atom in this sample,monoenergetically charged alpha (4He) and triton (3H) particlesemitted are shown in the reaction below:

6Li + n & 4He(2055 keV) + 3H(2727 keV) (1)

Fig. 2. A schematic layout of the cold neutron depth profiling chamber at NIST[adapted from [29]]. At the center of the chamber the sample is mounted usinga 21 cm diameter aluminum ring shaped disk concentrically covered with a thickdielectric sheet. The dielectric has a 1 cm diameter hole at the center of the diskwhich serves as the defining window for charged particles exiting from the samplein the direction of the detector.

The energy of the 4He and 3H particles at the reaction site is knownto be at 2055 keV and 2727 keV, respectively [9]. These heavycharged particles lose energy via a stochastic collision with elec-trons along the path traveling outwards. Both, the count rate andthe residual energy are simultaneously measured from all depthsfor the particle species emerging in the direction of the detector(Fig. 2). The charged particles do not lose any energy after leav-ing the surface of the sample traveling to the detectors, since thesample chamber is maintained at a vacuum less than 1.33 mPa(10"6 Torr). Calibration performed prior to the experiment deter-mined the full width half maximum (FWHM) energy resolution of18 keV for the charged particle detector. The samples were exposedto the neutron beam for various time lengths ranging between 3 and4 h. The exposure time was not fixed so the data was normalizedwith respect to the run time, but the samples were exposed longenough so that the statistical error in counting of the 4He or 3Hparticles is no higher than 3%.

The reaction center of mass is coincident with the site of thelithium atom. Thus the 4He and 3H particles originate from the samelocation as that of the original lithium atom, and their respectiveenergies are directly related to the location of the lithium atomin the sample. The energy loss of the charged particle per unitlength traveled through the sample is given by the stopping powerfunction of the sample. Mathematically, to the first-order approx-imation, the depth is related to the stopping power by Bragg’s lawgiven as:

x =! E0

E(x)

1S(E)

dE (2)

Here x is the path length traveled by the particle through the mate-rial, E0 is the initial energy of the particle, E(x) is the energy of theparticle emerging from the surface, and S(E) is the stopping powerof the sample material [15]. The Stopping and Range of Ions in Mat-ter (SRIM) code developed by Ziegler et al. [16] is then used to obtainthe stopping power of the LiFePO4 cathode and the graphite anodeand assign the residual energies of the charged particle to the cor-responding depth in the sample. The concentration of 6Li withinthe sample is determined by comparing the count rate observedfrom the sample with that of a well characterized boron concen-tration standard, labeled as N6 [28]. Since the natural abundance of

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6Li in the sample is only 7.5%, the total Li elemental concentrationis obtained by dividing the determined 6Li concentration by 0.075.

3. Results and discussion

The energy spectrum of the 2727 keV 3H particle is used herebecause of its two advantages over the corresponding energy spec-trum of the 2055 keV 4He particle. First, since the 3H particle hashigher energy and less mass, the concentration profiles can beobtained to greater depth in the sample. Second, 3H energy spec-trum is not overlapped by the 4He energy spectrum, but the 4Heenergy spectrum is interfered with by the 3H energy spectrum atlow energies, i.e., by the charged particles generated from deeperbelow the sample surface.

Fig. 3 shows the lithium concentration profile in the anode andcathode of the various cells aged with different C-rates. The lithiumprofile obtained from cell C0 is established as the baseline for com-parison. In the left column the lithium concentration profiles of theanode can be seen changing from section #1 to section #5 at thesame C-rate. The surface concentration increases across the dif-ferent cells with the C-rate. The right column shows the lithiumconcentration profile in the cathode. The profiles remain identicalfrom sections 1 to 5 at the same C-rate, but the slope of the profiledecreases with increasing C-rate.

Fig. 4 shows the effect of the SOC combined with the C-rate onthe lithium concentration profile. Fig. 4a shows the lithium con-centration profile in the cell cycled between 60% and 70% SOC with$6C-rate (C6) for sections #1, 3, and 5. The lithium concentrationprofile in cell C4 (same as in Fig. 3) is shown again in this figure forcomparison. In C6, even though the C-rate is high, the amount oflithium buildup near the surface of the anode is less as compared toC4. The prominent change of lithium concentration profiles in theanode from section #1 to section #5 observed in C4 is also absentin C6 except for minor deviations near the sub-surface. Similar toC4, the lithium concentration profiles in sections #1, 3, and 5 of cellC6 are identical to each other. However the lithium concentrationprofile for C6 has dropped below the concentration profile in C4.Thus, the overall lithium concentration in the cathode has droppedsignificantly in C6 as compared to C4. Thus at a higher SOC andmoderate C-rate, the lithium buildup on the surface of the anodeis contained, but lithium is lost from the host cathode material.In Fig. 4b the lithium concentration profile in section #5 of C16 iscompared with C0. In this case cell C16 is cycled between 45% and55% but with a very high C-rate of 16C. It should be noted that cellsC0 and C16 in this data were chosen from a different batch thanthe earlier cells. The basic chemistry was the same, but the ini-tial lithium concentration in the cathode was much higher in thesecells. The lithium buildup on the surface of the anode was very highin C16 compared to any other cell in this study. The concentrationin the anode dropped across its thickness with a steep slope. Thelithium concentration profile in the cathodes of cells C0 and C16are identical, but the concentration of lithium in the cathode wassignificantly lower than in C0. Thus, at moderate SOC but very highC-rate the process of lithium buildup on the surface of the anodeis enhanced while there is significant loss of lithium from the hostcathode. These results suggest that a cell operating at high SOC andmoderate C-rate has the least amount of lithium build up on theanode surface, and also the least amount of lithium is lost from thehost cathode.

Fig. 5 shows the lithium concentration profiles obtained on sec-tion #3 of cell C0 and C6 at various locations within the samesection. The aim here was to identify any change in the lithiumconcentration profiles measured at spots away from the center ofthe given section. The lithium concentration profiles in the anodeshown in the left column of Fig. 5 are similar for both cells at various

locations on section #3. This indicates that the lithium concen-tration in the anode does not vary along the height of the anode.The right column shows the lithium concentration profile in thecathode from both cells. The profiles for C0 measured at variouslocations on section #3 are identical, but the profile measured atthe center spot on the front side has a higher surface concentrationand shows a higher gradient along the thickness than at any otherlocation on the section #3. The profiles for C6 measured at variouslocations on section #3 are identical. Since the intensity and changein the lithium concentration in the unaged cell (C0) were greaterat the center of the section, the measurements were taken at thecenter of each section throughout this study.

As expected for a completely discharged unaged cell (C0) (Fig. 3),the lithium concentration in the anode is significantly lower withlittle buildup of lithium at the surface, while most of the lithiumis concentrated in the cathode. The lithium concentration pro-files in the anode show higher surface concentration as the C-rateincreases. The lithium concentration is at maximum near the sur-face, and it decays exponentially with the depth (thickness) ofthe sample. The lithium buildup on the anode surface from a cellcycled at higher SOC is less but increases with increasing C-rate.The lithium concentration drops in the cathode with higher SOCand higher C-rate. The lithium concentration profiles in the cath-ode show a uniform gradient, but the concentration decreases withincreasing C-rate.

The analysis of the surface lithium concentration in the anode isshown in Fig. 6. As seen in Fig. 6a the surface lithium concentrationis nearly constant over all the sections for C0 and C1. In the case ofC3 and C4 the surface lithium concentration increases from section#1 to section #5. Thus the buildup of lithium on the surface of theanode is greater towards the core of the cylindrical cell than againstthe outer edge. For example, in the case of cell C4 where the highestchange is observed, the concentration increases from 1.36 % 1020

to 3.74 % 1020 atoms/cm3 from edge to core. In Fig. 6b the effectof C-rate on the lithium concentration gradient in anode is shown.The lithium concentration gradient increases with the C-rate. Thelithium concentration gradient is very small in the case of cells C0and C1 and is very prominent in the case of cells C3 and C4. Thelithium concentration gradient in all cells exists only for a certaindepth from the surface of the anode. The depth up to which thelithium concentration gradient exists in the anode also increaseswith the C-rate. In the case of cell C4 the lithium concentrationgradient exists up to $1 !m in the anode. Thus with increasing C-rate not only does the lithium buildup on the surface increase, butthe lithium build up in the sub-surface area also increases.

It is well known that a solid electrolyte layer (SEI) composed ofthe decomposition products of the electrolyte salt and the solventis formed on the surface of the anode [17]. The thickness of the SEIis usually of the order of tens of nanometers [18,19]. This thicknessof the SEI on a given type of anode varies depending on the elec-trolyte components, mode of cycling, overpotential, temperature,etc. [20–23]. The lithium concentration profiles for the anode pre-sented here not only indicate higher lithium content in the SEI layerat higher C-rate, but also show that the lithium concentration in theSEI layer is changing from the outer edge to the core of the cylin-drical cell aged at a certain C-rate. This has never been reportedbefore in literature. This study reveals that the anode–electrolyteinterphase cannot be assumed to be alike over the length of theanode in a cylindrical cell as is the common practice adapted inLi-ion cell modeling. The analysis of the surface lithium concen-tration was also conducted and is presented in Fig. 7. A buildupof lithium on the surface as seen in the anode is not observed incathode samples from different cells. Since there is no buildup itis certain that there is no lithium plating occurring at the cathodesurface. The initial expectation was a decrease in the lithium con-centration in the aged sample as compared to the unaged sample.

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Fig. 3. Effect of C-rate on the lithium concentration in anode and cathode. The profiles were measured in all six sections from C0, C1, C3, and C4; only profiles over section1, 3 and 5 are shown here. Based on the Li concentration profile in the anode, the lithium tends to build up at the surface of the anode samples aged with higher C-rates,whereas the lithium concentration drops along the thickness of the cathode anode samples. The SOC varies from 0 to 10%.

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Fig. 4. Effect of state of charge (SOC) and C-rate on the lithium concentration profile in anode and cathode (a) in section #1, 3 and 5 from C4 and C6, and (b) comparisonbetween section #5 from C0 and C16. The lithium buildup on the anode surface from a cell cycled at higher SOC is less but increases with increasing C-rate. The lithiumconcentration drops in the cathode with higher SOC and higher C-rate. The SOC varies from 0 to 10% for C4, 45 to 55% for C6, and 60 to 70% for C16 during cycling of the cell.

The decrease in the lithium concentration in the case of cells C1,C3, and C4 (Fig. 3) is not very prominent, but the results in Fig. 4are in good agreement with this hypothesis. Therefore, there is acritical C-rate beyond which the drop in the lithium concentrationfrom the cathode is noticeable. In Fig. 7, the analysis of the lithiumconcentration gradient along the depth of the cathode is shownfor section #3 of different cells. The lithium concentration gradientobserved on a particular section decreases exponentially with theC-rate, as shown by the curve in Fig. 7. For example, in the case ofcells C0 and C4 the gradients are "1.63 % 1018 atoms/cm3/!m and"0.46 % 1018 atoms/cm3/!m. For a higher C-rate the concentrationgradient is lower, indicating that the flux available for diffusion of

lithium into the cathode particles is decreasing. Thus the furthercycling of the cells at still higher C-rate will be strongly affected.Since the concentration gradient has a negative slope, it indicatesthat the lithium diffusion within the LiFePO4 is restricted as the dif-fusion front moves towards the current collector. No fluctuationswere observed in the concentration profile as were observed byWhitney et al. [12]. Thus there is no structural breakdown of thecathode material, unlike that concluded by Whitney et al. [12].

The decrease in the lithium concentration can be explained bya change in the particle size. In previous studies by Nagpure et al.[6,24,7] the effect of LiFePO4 nanoparticles coarsening was reportedon the thermal diffusivity and electrical properties. The effects of

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Fig. 5. Lithium concentration profiles measured at different locations on section #3 in the anode and cathode of C0 and C6 cell. The profiles were measured at three differentspots along a straight line on one face (front) and on two spots on the opposite face (back). There is no change in the concentration profiles along the straight vertical line ina section.

coarsening of the LiFePO4 nanoparticles by sintering were alsoreported. The sintering of oxide particles usually takes place at hightemperatures, but in these nanoparticles, the onset of sintering atrelatively low temperatures may be attributed to the high surfaceenergy associated with the nanosize of the LiFePO4 particles. Dueto sintering of the nanoparticles, the effective surface area per unitvolume decreases, and correspondingly the porosity of the cath-ode decreases [25]. Also due to the coarsening of the nanoparticles,the diffusion length for the lithium increases within each particle.As a result, the net uptake of lithium during the discharging pro-cesses is low. During each charge cycle lithium diffuses out of theLiFePO4, and phase change occurs from LiFePO4 to FePO4. In thedischarge cycle the lithium diffuses back in the host FePO4 particle,and the phase changes from FePO4 to LiFePO4. During the early lifeof the battery the phase change from LiFePO4 to FePO4 and back toLiFePO4 might be complete, but as the particle size increases dueto coarsening, the diffusion length changes, and this will affect thephase change. The incomplete phase change continues to occur insubsequent cycles while the particle size tends to increase. Thus the

lithium retaining capacity of the particle drops in each subsequentcycle. The loss of active lithium in the cathode is directly related tothe drop in capacity of the battery while the increase in the particlesize and the subsequent increase in the diffusion length are directlyrelated to the rate capabilities of the battery.

To summarize, based on the results of this study, a schematicof the concentration profiles during the charging/discharging cycleand the concentration profile at the end of life is presented in Fig. 8.During the assembly of the cell the cathode is rich in lithium, andthe graphite anode is without any lithium (Fig. 8a). As the cell iscycled, the phase of the cathode changes from LiFePO4 to FePO4(Fig. 8b). According to Fuller et al. [26] the concentration profile oflithium in the solid electrodes and the electrolyte is given by:

"#ce

#t= D

#2ce

#x2 + aj(1 " t+) (3)

where " is the volume fraction of the phase, ce is the concentration,D is the diffusion coefficient, a is the specific area of the electrode, j isthe reaction rate, t+ is the transference number of Li, and x is the dis-

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Fig. 6. (a) Surface lithium concentration of the anode samples taken from cells agedwith different C-rate. The surface concentration increases linearly with C-rate. Thesurface concentration also increases from section #1 to #5 within a cell. (b) Lithiumconcentration gradient in section #3 of the anode samples taken from cells aged withdifferent C-rate. The concentration gradient increases with C-rate up to a certaindepth of the anode. The depth at which concentration gradient disappears increaseswith C-rate.

Fig. 7. Lithium concentration gradient in section #3 of the cathode samples takenfrom cells aged with different C-rate. The concentration gradient decreases withC-rate.

Fig. 8. Schematic for the buildup of lithium concentration at the anode surface andsimultaneous depletion of lithium concentration in the cathode at the end of life ofthe cell: (a) start of life, (b) charge/discharge cycle and (c) end of life.

tance along the thickness of the electrode. Based on this equation,the concentration gradient is dependent on the diffusion coeffi-cient and reaction rate. These parameters differ for the cathode andanode material.

Fig. 8c shows the schematic of the concentration profiles in theanode and cathode at the end of life. As suggested by Andersson andThomas [27], during charging/discharging of the cell, trapped, iso-lated zones of inactive LiFePO4 are formed resulting in incompletephase transformation and loss of the active lithium. On dischargingof the cell, the lithium from the anode re-enters the major volume ofthe FePO4 cathode, and the cathode phase changes to LiFePO4. Dur-ing the cycling process the particles appear to coarsen as suggestedearlier. The increased size of the particle increases the diffusionresistance for the lithium ions within the LiFePO4 cathode. Thus thecathode, instead of reaching the LiFePO4 phase, can only change toLi1"xFePO4 phase. The limiting diffusion within the cathode limitsthe diffusion of the lithium ions from the anode surface and theelectrolyte. As the diffusion within the electrolyte solution and thesolid phase graphite remains constant, the lithium starts to buildup on the surface of the anode. The lithium build up would increase

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in each subsequent cycle, consuming the active lithium and leadingto the loss of capacity.

The schematic in Fig. 8 is a simple description of the lithiumconcentration profile during charging/discharging of cells and atthe end of life. The schematic needs to be modified by consider-ing the concentration of Li in the electrolyte solution. Only thencan the mass balance equation be applied to the schematic, andthe net loss of the active Li can be calculated. The schematic alsodoes not help in identifying whether the aging is triggered by inef-ficiency of lithium ion diffusion in cathode or the coarsening ofthe cathode. However the data presented here provides quantita-tive measure of the lithium concentration profiles in the anode andcathode, which will prove instrumental in calibration of the Li-ioncell models.

4. Conclusions

The NDP technique was successfully applied to the study ofthe aging of LiFePO4 based lithium-ion batteries. The technique isshown to be efficient in determining the Li concentration to a usefuldepth of the electrode. Individual cells were aged at different ratesto different state of charge. The Li concentration profile across theelectrodes of the cells at the end of life is affected by the C-rate of thecharge/discharge cycle of the battery. The Li concentration profileis also affected by the state of charge of the cell. The Li concen-tration profile changes along the length of the electrode from outeredge to the core of the cylindrical cell, but it remains constant alongthe height of the electrode. In the case of anode, the lithium con-centration profile decays exponentially along the thickness of theanode. The Li builds up on the surface of the anode, and the builduprate increases along the length of the anode and also with the C-rate. This buildup below the surface extends to higher depth in cellscycled at higher C-rate. There is no buildup of the lithium near thecathode surface. Beyond a certain critical C-rate the lithium concen-tration drops with increasing C-rate, and it has a constant gradientalong the depth of the cathode. The gradient of the lithium con-centration profile in the cathode decreases with increasing C-rate.While the coarsening of the LiFePO4 particles limits the diffusion ofthe lithium in the cathode, the surface concentration of the lithiumon the anode increases with the C-rate. The quantitative measureof the lithium profiles for anode and cathode presented here willprove instrumental in calibrating the diffusion models of the Li-ioncells.

Acknowledgements

The authors sincerely thank the Institute for Materials Research(IMR) at The Ohio State University for providing the financialsupport for this research. The support of the National Instituteof Standards and Technology, U.S. Department of Commerce isacknowledged in providing the neutron research facilities usedin this work. The authors also thank Profs. Yann Guezennec andGiorgio Rizzoni for providing the Li-ion cell samples and technicaldiscussions. The authors would also like to thank Danyal Turkoglufor his support during the experiments.

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